Geotechnical Engineering

DHARM

190 GEOTECHNICAL ENGINEERING

Axis of radial

flow net

h=0

r=r¢ 0

h=ht

Fig. 6.25 Radial flow net for spherically radial

flow (After Taylor, 1948)

In this case also, practically all the head is lost in the final portions of the flow paths.

6.8 Methods of Obtaining Flow Nets

The following methods are available for the determination of flow nets:

1. Graphical solution by sketching


2. Mathematical or analytical methods


3. Numerical analysis


4. Models


5. Analogy methods
   All the methods are based on Laplace’s equation.

6.8.1 Graphical Solution by Sketching

A flow net for a given cross-section is obtained by first transforming the cross-section (if the
subsoil is anisotropic), and then sketching by trial and error, taking note of the boundary
conditions. The properties of flow nets such as the orthogonality of the flow lines and
equipotential lines, and the spaces being elementary squares, and the various rules concern-
ing boundary conditions and smooth transitions must be observed.

Sketching by trial and error was first suggested by Forchheimer (1930) and further
developed by A. Casagrande (1937). The following suggestions are made by Casagrande for the
benefit of the sketcher.

(a) Every opportunity to study well-constructed flow nets should be utilised to get the

feel of the problem.

(b) Four to five flow channels are usually sufficient for the first attempt.

(c) The entire flow net should be sketched roughly before details are adjusted.